In the past, skew and straight bevel gears have been designed to have line-contact between a gear and pinion. Here, the individual teeth of the gear and pinion interact with one another along lines of contact that shift along the face of the teeth as the gear and pinion rotate. However, errors in assembly or manufacturing, such as misalignment of the gear and pinion, can lead to the area of contact being transferred to the edges of the teeth. A transmission function φ2(φ1) of misaligned prior art gears is illustrated in FIG. 1. Angles φ1 and φ2 of transmission function φ2(φ1) represent angles of rotation of a prior art gear and pinion. Function φ2(φ1) exists as a sum of a linear function and a discontinuous almost linear function of transmission errors caused by errors of alignment. See “Gear Geometry and Applied Theory,” by F. L. Litvin, Prentice Hall (1994). Such transmission errors cause large acceleration when one pair of teeth is changed for another, resulting in inevitable vibration and noise of the gear drives.
Moreover, many of the existing skew and bevel gears are designed to be produced by cutting. The manufacture of gears produced by cutting is undesirable for at least two reasons. First, cutting the tooth surface does not guarantee reduction of noise and good bearing contact. Second, due to wear on the cutting tool, consistency between gear sets is difficult to obtain. As an alternative to cutting, forging of gears is preferred.
Forging is preferred over cutting because it allows the optimal geometry of gears to be chosen so as to improve bearing contact and reduce transmission errors. The optimal geometry can be easily obtained through the use of the proper dies. Application of the proper die geometry provides a localized bearing contact and a parabolic function of transmission errors. Such a parabolic function of transmission errors is able to absorb the linear function of transmission errors caused by misalignment and avoids the noise and vibration caused by misalignment. See “Gear Geometry and Applied Theory,” by F. L. Litvin, Prentice Hall (1994).